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We perform observational confrontation and cosmographic analysis of$f(T,T_G)$ gravity and cosmology. This higher-order torsional gravity is basedon both the torsion scalar, as well as on the teleparallel equivalent of theGauss-Bonnet combination, and gives rise to an effective dark-energy sectorwhich depends on the extra torsion contributions. We employ observational datafrom the Hubble function and Supernova Type Ia Pantheon datasets, applying aMarkov Chain Monte Carlo sampling technique, and we provide the iso-likelihoodcontours, as well as the best-fit values for the parameters of the power-lawmodel. Additionally, we reconstruct the effective dark-energy equation-of-stateparameter, which exhibits a quintessence-like behavior, while in the future theUniverse enters into the phantom regime, before it tends asymptotically to thecosmological constant value. Furthermore, we perform a detailed cosmographicanalysis, examining the deceleration, jerk, snap and lerk parameters, showingthat the transition to acceleration occurs in the redshift range $ 0.52 \leqz_{tr} \leq 0.89 $, as well as the preference of the scenario forquintessence-like behavior. Finally, we apply the Om diagnostic analysis, as across-verification of the obtained behavior.

Observational constraints and cosmographic analysis of $f({T},{T}_{{G}})$ gravity and cosmology